Average Error: 14.3 → 0.2
Time: 31.1s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}
double f(double x, double y) {
        double r374709 = x;
        double r374710 = sin(r374709);
        double r374711 = y;
        double r374712 = sinh(r374711);
        double r374713 = r374710 * r374712;
        double r374714 = r374713 / r374709;
        return r374714;
}
↓
double f(double x, double y) {
        double r374715 = x;
        double r374716 = sin(r374715);
        double r374717 = r374716 / r374715;
        double r374718 = 1.0;
        double r374719 = y;
        double r374720 = sinh(r374719);
        double r374721 = r374718 / r374720;
        double r374722 = r374717 / r374721;
        return r374722;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.3
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.3

    \[\frac{\sin x \cdot \sinh y}{x}\]
  2. Using strategy rm

  3. Applied associate-/l*0.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied div-inv0.9

    \[\leadsto \frac{\sin x}{\color{blue}{x \cdot \frac{1}{\sinh y}}}\]

  6. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}}\]

  7. Final simplification0.2

    \[\leadsto \frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))